Modeling of Transistor's Tracking Behavior in Compact Models

We present a novel method to model the tracking behavior of semiconductor transistors undergoing across-chip variations in a compact Monte Carlo model for SPICE simulations and show an enablement of simultaneous tracking relations among transistors on a chip at any poly density, any gate pitch, and any physical location for the first time. At smaller separations, our modeled tracking relation versus physical location reduces to Pelgrom's characterization on device's distance-dependent mismatch. Our method is very compact, since we do not use a matrix or a set of eigen solutions to represent correlations among transistors.